A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics

It's a very good book because if you want to learn black hole alone or I don't know I think calculate something, so it's for you. Moreover, the autor explain very simply the ideas that are difficult sometimes.

This is a great book, but don't expect it to be a general reference on the subject of general relativity. It is aimed at developing just what is needed for basic theoretical black hole mechanics. It does this admirably, with a minimum of mathematical fuss.

Everything OK !

This is one of the few book discussing the Gibbons-York-Hawking term. Also, shows the details to get the Hamilton equations from Hilbert's action

I started reading this book only yesterday. I've worked through all but the last chapter, and I'm already ready to conclude that this is an amazing book!This book is not for the beginner in relativity. The reason is that it takes you through a lot about GR which can (should, I say) be avoided in a first pass of GR. It is difficult to get the larger picture if you learning GR for the first time from this book. I therefore suggest, you should have had at least one course on GR. For those already adept in GR (say, by reading Carroll), this book is a gold mine.Rather than focusing on the physics behind GR (which it occasionally does though), it concerns itself with solving Einstein's equations and the various ways it can be set up. Thus, the book is exactly as it describes itself to be. It is a mathematical toolkit for people wishing to compute things in GR. What I like about it is that it works through a lot of dirty equations that other books avoid and relegate to references. This, for me is the most important factor.The first chapter quickly goes through some basic mathematics required. If you are reading this book, most of chapter 1 should already be familiar to you. Ch 2 discusses various geometrical aspects of curved spacetimes, such as the Raychaudhuri equations, the energy conditions, etc. Chapter 3 is a thorough discussion of hypersurfaces and its geometries. Ch 4 uses a lot of Ch. 3. Here the ADM formalism of GR is discussed. The final chapter (which I am yet to read) discussed black holes.

As the book title suggests, this is not an introduction to general relativity. However, with a basic understanding of general relativity and differential geometry, this book can be a very rewarding read. There are many other text books that cover the same material, but only superficially. This book fills in the gaps and provides the details that are indispensable for anyone doing research in the field or just seeking a deep understanding of general relativity. Explanations are concise and clear, with a logic that is sound and well-organzied. The chapter on the Lagrangian and Hamiltonian formulations of general relativity is the best I have seen in any book published so far; it provides the details that Wald and Carroll either neglect or gloss over in their textbooks. I only wish the book covered a few more topics. With only 250 pages, it can stand the addition of a few more chapters, perhaps on modified theories of gravity, initial value formulation, or advanced methods for solving the Einstein field equations.

The book has an interesting selection of topics, which can be used in realistic research problems. Everything is presented very lucidly, with all calculations given in detail. For example, you can learn the Hamiltonian formulation of GR in one day by working through Ch. 4 of the book.

This text is an advanced (graduate level) GR book. You'll need to have worked through an introductory book such as that by Bernard Schutz, "A first course in GR" or Hobson et al. "GR: An intro for physicists" before you can follow Poisson's book. A strong point is that Poisson gets straight to the point. Another unique feature is that detailed references for each subsection are provided that trace the origins of the arguments developed in the chapter. The exercises are challenging but informative. I find it takes some hard work to read this book but the effort is rewarded.

It's a good book.

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